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Decimals

Decimals connect fractions, percentages and money. Grammar school papers test decimal arithmetic, ordering and the trickiest skill: multiplying and dividing by decimals.

What is tested

  • Ordering and comparing decimals
  • Adding, subtracting, multiplying and dividing decimals
  • Converting between fractions, decimals and percentages

Worked example

Work out 3.4 × 0.6.

  1. Ignore the decimal points: 34 × 6 = 204.
  2. Count decimal places in the question: 1 + 1 = 2.
  3. Put 2 decimal places in the answer: 2.04.

Answer: 2.04

Exam-day checklist

  • Line up decimal points when adding or subtracting.
  • For multiplication, multiply as whole numbers then place the point.
  • Estimate to check the size (3.4 × 0.6 is a bit over 2).
  • To divide by a decimal, multiply both numbers by 10 or 100.

Common mistakes

  • Misaligning decimal points.
  • Thinking 0.45 is bigger than 0.5 because 45 > 5.
  • Losing a decimal place in a product.

Try it yourself

1. Work out 12.5 ÷ 0.5.

Show answer

25

Dividing by 0.5 is the same as multiplying by 2: 12.5 × 2 = 25.

2. Work out 0.7 + 0.45.

Show answer

1.15

0.70 + 0.45 = 1.15.

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More topic guides

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